The resolution of a ground-based large-scale aperture telescope can be severely deteriorated by atmospheric turbulence. Adaptive optics (AO) systems have been widely used thus far to solve this problem. However, correction using AO is a partial solution. Degraded images generated by residual wavefronts can be restored via post-reconstruction. In this paper, a blind deconvolution algorithm to improve the quality of Poisson noise astronomical images acquired after AO correction is proposed. The algorithm uses an adaptive L1 norm term in the gradient domain for an accurate estimation of the point spread function (PSF) as well as the Richardson-Lucy algorithm followed by a low pass denoising filter to solve Poisson deconvolution. Experimental results for simulated and real astronomical images demonstrate that the proposed algorithm can obtain better PSF and reconstruction images than other algorithms and significantly improves the quality of post-AO astronomical images without further information.